Department of Mathematics students conduct significant research in an in-house SOAR program and in Research Experiences for Undergraduates (REU) programs across the country. Our students present findings in poster sessions at the Joint Mathematics Meetings hosted by the American Mathematical Society (AMS) or at Mathfest hosted by the Mathematical Association of America (MAA).
Established in 2008, the SOAR Program is an opportunity for students in the Department of Mathematics at Grove City College to participate in a short-term, focused research project. For about four weeks each summer, the College invites two or three math students to work on a research project. The SOAR Program is generously funded by Grove City College's Swezey Fund for Scientific Research and Instrumentation. The Department of Mathematics continues the SOAR Program based upon adequate levels of support.
Polytope Number Sequences
Polytope number sequences are sequence created from the geometry of polytopes. These sequences have interesting connections to each other and to a variety of classical combinatorics topics such as binomial coefficients and Eulerian numbers. Students have found patterns in the sequences while working with families of polytopes.
Topological Data Analysis
Topological data analysis is a process of finding shape in complicated data. Students are working to apply the techniques of topological data analysis to areas including congressional redistricting, musical analysis, the motion of swimming fish, and fluid dynamics.
Students are studying a new type of non-Euclidean geometry created from exponential and power functions. The students are studying how this new geometry is similar to the standard types of geometry including Euclidean, spherical, and hyperbolic. They are endeavoring to prove theorems to show these relationships.
Networked Control Systems (NCS)
Networked control systems (NCS) are a type of distributed control systems where sensors, actuators, and other devices are interconnected. The study of NCSs is an interdisciplinary research area with applications in many fields like sociology, political science, biology, robotics, and computer science. The students are attempting to formulate and answer precise questions using computer simulations and mathematical reasoning using linear algebra, graph theory, and differential equations.
Our students have participated in REU programs across the country including: